The mean of a normally distributed dataset is 12, and the standard deviation is 2.
2 answers:
Answer:
95.44% of the data lies between 8 and 16.
Step-by-step explanation:
Since, z score or standard score formula is,
Where,
= mean of the data,
= standard deviation,
Let X represents a data point,
So, we have to find out,
P( 8 < X < 16),
Since,
( By the z-score table )
Hence, 95.44% of the data lies between 8 and 16.
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1. Notice that dividing both sides of by 2 returns
, same as the first equation. So the system of equations reduces to one equation, which can have an infinite number of solutions. (This is because for any choice of
or
, you can always find a corresponding value for the other variable.)
2. See attached image. is given by the purple line.
For 3-6, you have several options. The two simplest methods of solving them are by substitution or elimination.
3. Like with (1), notice that dividing both sides of the first equation by 2 gives , so there will be an infinite number of solutions.
4. (by substitution) Since , we can replace
in the second equation:
but this is false, so there are no solutions to this system.
5. (by substitution) Since , in the first equation we have
Then back in the second equation we find
So (-4, -3) is the only solution here.
6. (by substitution) Notice that the left hand sides of both equations are the same, so we end up with 7 = 12, but this is false, so no solution exists.
